Actually, Star Trek: Birth of the Federation had a campaign multiplayer. It may get annoying to wait for eachother's turn to end, but like BOTF you could just have a save option so the players can pick up later. It may take a while, but the fun factor of running a multiplayer campaign over a few weeks is well worth it.

Anyway, the battles could be less monotonous too. If you simply let each player run his battles at the same time on the individual computers, there would be virtually no time lost between turns unless one player is playing an epicly huge battle and the other is fighting a sole unit of peasants. If no battle occurs for you in a turn, perhaps the non-battle players can be given the option to watch another player's battle instead of waiting around twiddling their thumbs?

Anyway, it's completely do-able, and I've done it before with BOTF which requires a heck of a lot more micromanaging the RTW.